OK, I'll admit it. None of us are investment guru and haven't made (or lost) millions
playing the stock market. However, we've been asked a few times to work on projects
related to automated trading systems and these are some of the books we found most
interesting or useful. Click on the titles to see reviews by other people and other
information from your local Amazon.

The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward
Richard L. Hudson, Benoit B. Mandelbrot, Basic Books
One of the key assumptions made by many investment and pricing theories (e.g. BlackScholes)
is that prices behave in a manner which can be modelled by the normal distribution. It seems
on the face of it a reasonable assumption, but it isn't.
Mandelbrot makes a strong case that the normal distribution is a poor estimator
for the distribution of price changes, and that a fractal distribution paints a more
accurate picture. Why does it matter? If you take the normal assumption then
large jumps in price are extremely unlikely, and price changes on any day are not
affected by changes the previous day. In fact the extremes do happen, and the
magnitude of today's changes does correlate with previous day's trading. The net effect
is that the normal distribution assumption seriously underestimates risk.
This book is in the popular science category. There is no deep mathematics
or equations. (A shame, if you are mathematically inclined — good news, if you
aren't.) There's a reasonable mix of anecdote and experimental evidence,
but a little too much schadenfreude when Mandelbrot manages to prove
himself right and others wrong.
This book won't make you rich, or give you a surefire way of making money on
the markets — it's author carefully points this out. What it will give you
is a deeper understanding of the shaky foundations on which portfolio theory,
option pricing and many other models are based, as well as some ideas on how
to more realistically test a trading system on simulated data.
Other Reviews
R2012.792004

Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win (Outlooks)
Steven Skiena, The Mathematical Association of America
If you've ever dreamed of creating a computer system to beat the bookies or the
stock market (and who hasn't?) then Steven Skiena's book is for you. Skiena describes
his own (and his team's) efforts to create an automated system which would place
winning bets on jai alai, a Basque game which is also played in parts of
France and some cities in North America. The book describes the game itself
(a game with similarities to tennis, squash and rugby fives), the convoluted methods
by which tournaments are held (a sort of round robin) and the parimutuel gambling
system which is used to place bets on the outcome.
To create the perfect system, Skiena and his team needed to model the tournament
structure, the effects of player skill on match outcomes,and (since this the
odds are offered using a parimutuel system) the betting habits of the general
public. They then needed to identify bets which would (on average) be profitable.
The team succeeded, the program they developed ultimately succeeding in returning
about 500% on its initial gambling stake in a single year. (The bad news, as Skiena
points out, is that it would not be possible to use such a system to bet large amounts
of money on jai alai, since such bets would significantly depress the odds available).
A must read for anyone seriously interested in "beating the system".
Other Reviews
R2012.662001

A Mathematician Plays The Stock Market
John Allen Paulos, John Allen, Basic Books
Paulos lost money on the WORLDCOM crash, and uses this as a jumping off point for explaining
the mathematics behind the stock market. There are good qualitative explanations of many
of the numbers and theories used in attempting to predict the price of stocks. I especially liked
his description of the Efficient Market Hypothesis Paradox (if everybody believed in it,
the Efficient Market Hypoethesis would no longer be true) and its imaginary opposite,
the Sluggish Market Hypothesis.
Another good point he makes is that the criteria for success of a trading system is not
whether it makes money. That's only a necessary condition. A successful trading system
must make more money than simply investing in treasury bills, or buying an index
fund.
The book covers in outline such subjects such as technical analysis, beta, portfolio
theory, etc.
Although there are some excellent nuggets of information here, I found the writing style
distracting. I was also disappointed that another book
by the same author (Once upon a number : the hidden mathematical logic of stories)
covered much of the same ground with the same examples.
Other Reviews
R2011.842003

Reminiscences of a Stock Operator
Edwin Lefevre, John Wiley & Sons
Judging by this autobiography Edwin Lefèvre (a penname of
Jesse Livermore) may have been the sort of person your mother warned you against.
He made his living from speculating on the stock market, sometimes using techniques which
would probably be illegal today. He both won and lost money, and this book
contains his insights into successful and unsuccessful trading periods. Here's
one of Lefèvre's asides on the nature of speculation, which follows
a story of a man who had a successful system, thought he could do better by
changing the system, then wiped himself out:
I sometimes think that speculation must be an unnatural sort of business,
because I find that the average speculator has arrayed against him his own nature.
The weaknesses that all men are prone to are fatal to success in speculation —
ususally those very weaknesses that make him likable to his fellows or that he himself
particularly guards against in other ventures of his where they are not nearly so
dangerous as when he is trading in stocks or commodities.
Perhaps an automated system will not be subject to such human mistakes? Or will it,
too, lack the humility of traders such as Taleb?
Other Reviews
R2011.611994

Computerized Trading: Maximizing Day Trading and Overnight Profits (New York Institute of Finance)
Mark Jurik, Jurik, New York Institute of Finance
Lacking the modesty or limited objectives of either Taleb or
Paulos, this book claims it will reveal ... how you
can use your computer to gather, analyze, and detect profitable market inefficiencies —
the key to making winning trades day after day.
Yes, really.
Despite this publishing hyperbole, there is much to recommend this book if you are
planning on implementing a trading system. There are explanations of neural net,
technical analysis, and data mining approaches. There are also descriptions of two or
three major projects, discussions of possible commercial data sources, and key
questions to ask in evaluating systems.
Some of the chapters in this book are somewhat dated: with the substantial changes
in hardware and software since 1999 we thankfully don't have to worry anymore about
whether incoming data will overflow our 16550 UART. However, many design considerations
never change and this book is still worth a read if you are considering designing or
evaluating an automated trading strategy.
Other Reviews
R2010.741999

Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets
Nassim Nicholas Taleb, Texere
This book contains musings on random events and its effects on the market (and life
in general) by a professional trader, Nassim Taleb. There are thoughts here which
I found quite profound concerning the nature of inductive logic (reasoning from
events to rules), as well as interesting examples and explanations of how we allow
ourselves to be fooled by random phenomena.
Taleb is particlarly fascinated by what he describes as the Black Swan Problem.
We see lots of swans. All of them are white. We infer that all swans are white.
Unfortunately we have never been to Australia, where the swans are black as well. If
we build our trading systems on such principles will the appearance of a black swan
wipe us out?
The style of writing here is collection of literate musings and digressions which
I rather liked but, judging by Amazon reviews, it appears to irk some readers.
Other Reviews
R2009.612004

Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
William Poundstone, Hill and Wang
If you can survive reading the title, this book is actually an anecdotal history of the Kelly Criterion — a formula which identifies how much should be wagered on a risky undertaking. A surprising cast of characters is involved, from underworld figures to physicists and mathematicians, and from 1738 (not a misprint) to the present day.
This isn't a mathematical enough treatment for me, but it's well worth reading to find out how people have tried and succeeded (or failed) in exploiting Kelly's (and Bernoulli's) work.
(If you need to play around with numbers, the Kelly Calculator may be useful.)
Other Reviews
R2009.012006